I grew up in America, but my parents are both from Iran. My Persian is not terribly strong (probably 3-4 grade level as well), but I try to exclusively speak it to my kids. I find it challenging at times, particularly because there is much more English around them than Persian (friends, in-laws, TV, my wife). But the benefits for my children are worth the effort for me.
For me the goal is not necessarily to get them to the point of fluency (even though that would be nice). Language proficiency is a sufficient goal. They may not be able to carry on a technical discussion, but as adults they could perhaps know enough to carry on simple conversations.
Aside from my personal goals, there are linguistic and cognitive benefits to learning multiple languages from an early age. The cognitive benefits of learning multiple languages from an early age are explained by The American Council on the Teaching of Foreign Languages:
Children who learn a foreign language beginning in early childhood demonstrate certain cognitive advantages over children who do not. ... Additionally, foreign language learning is much more a cognitive problem solving activity than a linguistic activity, overall. Studies have shown repeatedly that foreign language learning increases critical thinking skills, creativity, and flexibility of mind in young children. Students who are learning a foreign language out-score their non-foreign language learning peers in the verbal and, surprisingly to some, the math sections of standardized tests. This relationship between foreign language study and increased mathematical skill development, particularly in the area of problem solving, points once again to the fact that second language learning is more of a cognitive than linguistic activity.
Another study finds:
Italian psychologists Agnes Melinda Kovacs and Jacques Mehler have found that part of [bilingual childrens'] skill lies in being more flexible learners than their monolingual peers. Their exposure to two languages at an early point in their lives trains them to extract patterns from multiple sources of information.
Here are some things you can do:
- Spend as much time as you can around native speakers (family, friends, church, temple, cultural organizations, etc.)
- Make a concerted effort to improve your language skills by learning vocabulary that is pertinent to common dialog you have with your children (focus on commands, household objects, animals, etc.)
- Keep a notebook near you and every time you can't remember a word you want to use with your child, write it down. Go ahead and use the English (or other language) word so you can complete your thought with your child. Then, after you learn the Mandarin word, make sure you use it from them on.
- Find a list of most commonly used conversational words in Mandarin and make sure you know the first 300-500.
- Put your child in language classes as soon as they're old enough (5-6 yo).
- Play "What is this?" with your child. Point to things and have your child tell you what they are. Using flashcards works well too. I'm sure you can buy Chinese flashcards online.
- Get some Chinese-language kids TV shows and cartoons that you can play for you child when he gets a little older.
- Make a commitment to your spouse that you will only speak Mandarin in front of your child. Struggle through it and you guys will notice that you're getting better.